一类非线性抛物方程的有限元分析

Analysis of a Finite Element for a Nonlinear Parabolic Equation

利用双线性元给出一类非线性抛物方程的有限元逼近格式,在半离散格式和线性化的向后欧拉全离散格式下得到了原始变量u的H^1模的O(h^2)阶和O(h^2+τ)阶的超逼近性质(h、τ分别表示空间剖分参数和时间步长),最后给出了一个数值算例加以验证.

With the help of the bilinear element,a finite element approximation scheme is proposed for a nonlinear parabolic equation.The superclose of order O （h2） and O （h2＋ τ） are obtained for original variable u in H^1 norm under semi-discrete scheme and linearized form backward Euler fully-discrete scheme （h and τ are parameters of subdivision in space and time step）.Finally,a numerical experiment is provided to confirm the theoretical analysis.